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Monotonic Stack Fundamentals Monotonic stacks enable linear preprocessing to find: Prefix/suffix maximum/minimum positions in sequences Next greater/smaller element positions for each index Problem B3666: Suffix Maximum Positions Given a dynamically growing array, after each insertion, find all suffix maximum indices and output their XOR sum. ...

A. Cosmic End Find a number within a given range that is the product of three distinct primes. Given the small constraitn (upper bound ≤ 100), precompute small primes and check all combinations of three distinct ones. The maximum third prime needed is around 100/(2×3) ≈ 16, so checking primes up to 19 suffices. #include <bits/stdc++.h> us ...

Problem A: Rope Cutting Condition The task requires determining how many ropes must be severed based on their attachment points. Each rope connects a nail at height a to a branch at height b. A cut is mandatory whenever the nail is positioned strictly higher than the branch. The algorithm iterates through all given pairs, evaluates this inequal ...

A – Two Rectangles [Max Area Logic] Given the dimensions of two rectangles: Rectangle 1: (A \times B) Rectangle 2: (C \times D) Determine and output the larger area. Tie-breaking is irrelevant. i64 a, b, c, d; std::cin >> a >> b >> c >> d; i64 r1 = a * b, r2 = c * d; i64 best = (r1 >= r2) ? r1 : r2; std::cout <&l ...

Problem Statement Given an n×m integer matrix and q queries, each query specifies the coordinates of the top-left and bottom-right corners of a submatrix. For each query, compute the sum of all elements within the specified submatrix. Solution Approach The problem can be efficiently solved using 2D prefix sums. By precomputing the cumulative su ...

Linear Operation Segment Trees The most basic form of segment tree handles linear operations that satisfy commutativity and associativity, such as addition. Since operations do not depend on each other, maintaining lazy propagation is straightforward. For single-point modifications, a Fenwick Tree (Binary Indexed Tree) is often a more efficient ...

Problem A: Strategic Allocation This challenge involves selecting a subset of items to meet a weight capacity requirement with the minimum count. The optimal approach utilizes a greedy strategy. By prioritizing larger weights first, we minimize the number of items required to reach the target threshold. void processAllocation() { int itemCo ...

Display the first N+2 digits of π (including the decimal point). #include <iostream> #include <string> const std::string PI_DIGITS = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679"; int main() { int digits; std::cin >> digits; std::cout << P ...

1. Prefix Sum Technique 1.1 One-Dimensional Prefix Sum The prefix sum algorithm is an optimization technique used to calculate the sum of elements within a specific range $[L, R]$ in $O(1)$ time after an $O(N)$ preprocessing step. In a naive approach, calculating range sums repeatedly would result in $O(N \times M)$ complexity for $M$ queries; ...

Mathematical Caclulation Problem Given the formula for distance between a point and a line, we can simpliyf the calculation to |x-y| * 50: #include <iostream> #include <cmath> int main() { int x, y; std::cin >> x >> y; std::cout << abs(y - x) * 50 << '\n'; return 0; } String Output Problem S ...